We study Rnyi entropies for geometries with Lifshitz scaling and hyperscaling violation. We calculate them for specific values of the Lifshitz parameter, and analyze the dual spectrum of the ground state. In the large d − θ limit they show that the ground state is unique in specific parameter ranges. We also calculate the Rnyi entropies perturbatively around n = 1, and derive constraints using the Rnyi entropy inequalities, which correspond to the thermodynamic stability of the black holes.

中文翻译：

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关于 Lifshitz 的 Rnyi 熵和超尺度违反黑洞

我们研究了具有 Lifshitz 标度和超标度违规的几何的 Rnyi 熵。我们针对 Lifshitz 参数的特定值计算它们，并分析基态的双谱。在大的d - θ限制中，它们表明基态在特定参数范围内是唯一的。我们还在n = 1附近微扰地计算 Rnyi 熵，并使用 Rnyi 熵不等式导出约束，这对应于黑洞的热力学稳定性。